Binary Fields on Limited Systems

TL;DR

This paper introduces resource-efficient algorithms for binary field computations suitable for small, limited systems, with applications in cryptography, improving upon existing prime field algorithms.

Contribution

It presents new algorithms optimized for binary field arithmetic on limited-resource systems, enhancing computational efficiency in cryptographic applications.

Findings

Increased efficiency over previous algorithms

Effective for small, resource-constrained machines

Applicable to cryptographic computations

Abstract

The intrinsic structure of binary fields poses a challenging complexity problem from both hardware and software point of view. Motivated by applications to modern cryptography, we describe some simple techniques aimed at performing computations over binary fields using systems with limited resources. This is particularly important when such computations must be carried out by means of very small and simple machines. The algorithms described in the present paper provide an increased efficiency in computations, when compared to the previously known algorithms for the arithmetic over prime fields.